Question

A circle has centre C(2,3) and a radius of 5 units. This is defined by the equation (x-2)²+(y-3)²=25

a. Determine the y coordinates of the end points on the circle that has x=6

Answer 1

The y-coordinates of the endpoints on the circle at x=6 are 6 and 0.

Step-by-step explanation:

To determine the y-coordinates of the endpoints on the circle with a center C(2,3) and radius of 5 units at the given x=6, we plug x=6 into the circle's equation:

(x-2)² + (y-3)² = 25

Substituting x=6, we get:

(6-2)² + (y-3)² = 25

16 + (y-3)² = 25

(y-3)² = 9

Thus, y-3 = ±√9

So the two possible values for y are:

• y = 3 + 3
• y = 3 - 3

Therefore, the y-coordinates are 6 and 0.